sloppycanada
  • sloppycanada
Find f(g(x)) if f(x) = 2x + 1 and g(x) = x2 - 1.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Jhannybean
  • Jhannybean
Wherever you see an x in your function for f(x) replace it with the function of g(x). \[f(g(x)) = 2(x^2-2)+1\]
anonymous
  • anonymous
did u understood?
sloppycanada
  • sloppycanada
\[2x^2-3\] @Jhannybean

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sloppycanada
  • sloppycanada
but that's not one of my choices.
Jhannybean
  • Jhannybean
What are your answer choices?
anonymous
  • anonymous
ok \[f(g(x))= 2(x ^{2}-1)+1\]
anonymous
  • anonymous
\[f(g(x))=2x ^{2}-2+1\]
anonymous
  • anonymous
2(x^2-1)+1 = 2x^2 -2 + 1 = 2x^2 - 1
Jhannybean
  • Jhannybean
Oh, I made a typo there.
Jhannybean
  • Jhannybean
The \(x^2-2\) should have been \(x^2-1\)
anonymous
  • anonymous
\[f(g(x))= 2x ^{2}-1\]
anonymous
  • anonymous
hope this helps :)
Jhannybean
  • Jhannybean
No harm in correcting me :)
anonymous
  • anonymous
f(g(x)) = 2(g(x)) +1 = 2(x^2-1)+1
sloppycanada
  • sloppycanada
So this one - Find g(f(x)) if f(x) = 2x - 3 and g(x) = x - 1.
sloppycanada
  • sloppycanada
Should be - \[2x^2 + x -3\]
anonymous
  • anonymous
g)x)-1 = (2x-3)-1 = 2x-4
sloppycanada
  • sloppycanada
Find f(g(x)) if f(x) = 2x + 1 and g(x) = x2 - 1. My answer options are - 2x -1 \[2x^2-1\] \[2x^2 + 1\] \[2x^3-1\]
sloppycanada
  • sloppycanada
So if it's f(g(x)), shouldn't it be something along the lines of - (x^2 - 1)(2x+1)?
Jhannybean
  • Jhannybean
We've done this one.
Jhannybean
  • Jhannybean
Just scroll up?
sloppycanada
  • sloppycanada
It's just 2x -1 ?
Jhannybean
  • Jhannybean
You're not multiplying anything actually, you're just substituting the function of g(x).
sloppycanada
  • sloppycanada
Wait what? I am very confused.
Jhannybean
  • Jhannybean
\[f(g(x))= f(x^2-1) = 2(x^2-1)+1 = 2x^2-2+1 =2x^2-1\]
Jhannybean
  • Jhannybean
Do you see it now, @sloppycanada ?
sloppycanada
  • sloppycanada
Kind of..
Jhannybean
  • Jhannybean
which part is confusing you?
sloppycanada
  • sloppycanada
Where the "x" in 2x-1 went.
Jhannybean
  • Jhannybean
It was replaced by g(x)
sloppycanada
  • sloppycanada
Okay, so in this - Find g(f(x)) if f(x) = 2x - 3 and g(x) = x - 1. It'd just be 1(2x -3) - 1?
Jhannybean
  • Jhannybean
Not quite, \[g(f(x)) = g(2x-3)= (2x-3)-1 = 2x-4\]
sloppycanada
  • sloppycanada
Okay so again - Find (f – g)(x) if f(x) = 2x – 6 and g(x) = 3x + 8. (2x -6) - (3x+ 8) = -x +2?
Jhannybean
  • Jhannybean
Somewhat, but a small math error. \[(f-g)(x) = f(x) - g(x) = (2x-6)-(3x+8) = -x-(8+6) = -x-14\]
Jhannybean
  • Jhannybean
You've got the idea though :D
sloppycanada
  • sloppycanada
Find (f + g)(x) if f(x) = 1/2x + 4 and g(x) = -x - 3. (1/2x +4) + (-x-3) = -1/2 + 1
sloppycanada
  • sloppycanada
-1/2x* +1?
Jhannybean
  • Jhannybean
Yep
sloppycanada
  • sloppycanada
Find the zeros of -4x + 6

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